To avoid biasing inferred cosmological parameters obtained through the matter two-point correlators, we must account for the effect of baryons on the matter distribution.
Baryons modify the dark-matter-only (DMO) halo profile in several ways, which has been explored in detail (e.g. [1]}, [2]}, [3]}, [4]}, [5]}).
In the presence of baryons, gas and stars must be accounted for in the halo profile in addition to dark matter.
AGN and supernova feedback effects also move gas away from the halo center, which redistributes dark matter within the halo profile.
From the perspective of the HZPT model, the effect of baryons should only be to modify the BB terms (see Appendix REF  for an illustrative calculation using halo profiles).
Baryons should not affect the large scales relevant for the halo compensation \(R\)  or the one-halo amplitude \(A_{0}\) , assuming conservation of mass between the DMO and DM+baryon scenarios (up to two-fluid corrections in the ZA [6]}, [7]}, [8]}, [9]}).
This is the same rationale used to motivate scale cuts (e.g. [10]}).
MS14 fitted changes in the power spectrum due to a single AGN model of feedback in the coefficients for the first three terms of the \(k^{2}\)  profile expansion up to \(k=0.8\ h/\rm {Mpc}\) .
They found that the change in \(A_{0}\)  (which is the same as our \(A_{0}\)  up to small changes due to the compensation term) is almost an order of magnitude lower than changes in the higher-order parameters, which change at the \(\sim 5\% \)  level, and if they fix \(A_{0}\)  the change in the other terms is larger but still effectively captured by the profile expansion.
